" If "[x+[2x]]<3," where [.]denotes the greatest integer function,then "x" is "

If f(x)={:{(2x", if " x lt 2),(2", if " x=2),(x^(2)", if " x gt2):} , then

|[x+lambda, 2x, 2x], [2x, x+lambda, 2x], [2x, 2x, x+lambda]| =(5x+ lambda)(lambda-x)^(2)

The value of x, if 2^(x)+2^(x)+2^(x)=192 is

Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

det [[x + 4,2x, 2x2x, x + 4,2x2x, 2x, x + 4]]

Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x)^2

|[x+4,2x,2x] , [2x,x+4,2x] , [2x,2x,x+4]|=(5x+4)(x-4)^2

By using properties of determinants, show that : |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]| = (5x+4)(4-x)^2

The LCM of the polynomials (x^(2) + x - 2) (x^(2) + x -a) and (x^(2) + x -b) (x^(2) + 5x + a) " is " (x -1) (x +2) (x +3) , then find the values of a and b